If ΔPQR ≅ ΔABC , AB = 6 cm, ∠B = 50° and ∠A = 70°, then which of the following is true?

Correct — D. Read the congruence in the order it is written: ΔPQR ≅ ΔABC pairs P with A, Q with B, R with C.

Sides pair the same way, so PQ answers to AB.
AB = 6 cm → QP = 6 cm

Angles pair the same way, so ∠R answers to ∠C.
∠C = 180° − 70° − 50° = 60° → ∠R = 60°

Both halves of option (d) hold.

Why the others are wrong

• (a)
  Option (a) claims QR = 6 cm. QR answers to BC, and BC is never given — only AB is 6 cm. Its angle half is right, but the side is not.
• (b)
  Option (b) fails twice over. QR is not the side that answers to AB, and ∠Q = ∠B = 50°, not 60°.
• (c)
  Option (c) has the side right and the angle wrong: ∠P answers to ∠A, so ∠P = 70°. The 60° angle belongs to R.

A congruence statement is an ordered statement. ΔPQR ≅ ΔABC says more than that the triangles match — it says which vertex answers to which, first to first, second to second, third to third.

Everything else follows from that ordering: PQ = AB, QR = BC, RP = CA, ∠P = ∠A, ∠Q = ∠B and ∠R = ∠C.

The arithmetic is just the angle sum. Two angles of ΔABC are given, so the third is 180° − 70° − 50° = 60°.

Key facts

• In ΔPQR ≅ ΔABC the correspondence is P to A, Q to B and R to C, taken in the written order.
• Corresponding sides are therefore PQ = AB, QR = BC and RP = CA.
• With ∠A = 70° and ∠B = 50°, the third angle ∠C is 60°, so ∠R = 60°.

Common traps

• Matching letters alphabetically instead of by position, which pairs QR with AB
• Attaching the 60° to ∠P or ∠Q rather than to ∠R

No directly related past PYQ was found.